Stream velocity from symmetric 1 km runs: A person rows 1 km downstream in 10 minutes and 1 km upstream in 30 minutes. Find the velocity of the stream.

Introduction / Context:Equal distances with different times give direct speeds. Convert minutes to hours, compute the downstream and upstream speeds, then extract the stream speed via half-difference.

Given Data / Assumptions:

• Downstream: 1 km in 10 min = 1 km / (10/60 h) = 6 km/h.
• Upstream: 1 km in 30 min = 1 km / (30/60 h) = 2 km/h.
• u is still-water speed; v is stream speed.

Concept / Approach:Use v = (down − up)/2; u = (down + up)/2.

Step-by-Step Solution:Down = 6, Up = 2.v = (6 − 2) / 2 = 2 km/h.u = (6 + 2) / 2 = 4 km/h (for reference).

Verification / Alternative check:Check composition: u + v = 6, u − v = 2 matches the given.

Why Other Options Are Wrong:1, 3, 4, 1.5 do not equal the required half-difference.

Common Pitfalls:Using average instead of half-difference for v; forgetting to convert minutes to hours correctly.

Final Answer:2 km/hr